A State Space Modeling Approach for Time Series Forecasting

Abstract

A stochastic filtering method is presented for on-line recursive estimation and forecasting of autocorrelated time series. Several state space models for nonseasonal and seasonal time series, which belong to the autoregressive integrated-moving average class, are presented. The Kalman filter is introduced as the recursive data processor for on-line time series forecasting. The estimation problem and initial values determination are discussed, and numerical examples are given. An extension of Brown's adaptive smoothing method for autocorrelated time series through the proposed filtering approach is also presented.